A Potential Tale of Two by Two Tables from Completely Randomized Experiments

TL;DR

This paper explores causal inference in randomized experiments with binary outcomes, proposing new asymptotic and Bayesian methods that address limitations of traditional assumptions and improve inference accuracy.

Contribution

It introduces novel asymptotic and Bayesian procedures that account for non-additive causal effects, enhancing inference in binary outcome experiments beyond existing methods.

Findings

Proposed methods outperform traditional approaches in simulations.

New procedures are applicable to both linear and non-linear estimands.

Theoretical and simulation results validate the superiority of the proposed methods.

Abstract

Causal inference in completely randomized treatment-control studies with binary outcomes is discussed from Fisherian, Neymanian and Bayesian perspectives, using the potential outcomes framework. A randomization-based justification of Fisher's exact test is provided. Arguing that the crucial assumption of constant causal effect is often unrealistic, and holds only for extreme cases, some new asymptotic and Bayesian inferential procedures are proposed. The proposed procedures exploit the intrinsic non-additivity of unit-level causal effects, can be applied to linear and non-linear estimands, and dominate the existing methods, as verified theoretically and also through simulation studies.